Generating a defined set of genetic constructs within a large combinatorial space provides a powerful method for engineering novel biological functions. However, the process of assembling more than a few specific DNA sequences can be costly, time consuming and error prone. Even if a correct theoretical construction scheme is developed manually, it is likely to be suboptimal by any number of cost metrics. Modular, robust and formal approaches are needed for exploring these vast design spaces. By automating the design of DNA fabrication schemes using computational algorithms, we can eliminate human error while reducing redundant operations, thus minimizing the time and cost required for conducting biological engineering experiments. Here, we provide algorithms that optimize the simultaneous assembly of a collection of related DNA sequences. We compare our algorithms to an exhaustive search on a small synthetic dataset and our results show that our algorithms can quickly find an optimal solution. Comparison with random search approaches on two real-world datasets show that our algorithms can also quickly find lower-cost solutions for large datasets.